Re: r-Squared Question

In article <1121175957.796245.150510@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Predictor <predictr@xxxxxxxxxxxxxxxx> wrote:

>I am trying to undertand r-squared (the coefficient of determination)
>of regression lines. If r, which is squared to obtain r-squared, is
>the correlation between the predicted Y and the observed Y, then
>doesn't that mean that any regression line whose predicted Y is a
>perfect linear function of the observed Y has an r (and thus r-squared)
>of 1?

That's true. You may be a bit confused, however. The only way that
the predicted and observed Y can be related by a linear function is if
the predicted and observed Y are identical (ie, the linear function is
observed=predicted). You may be confusing "predicted value" with
"predictor" (also known as a covariate or explanatory variable). The
predicted value is the linear function of the covariates in which the
coefficients are those found by fitting to the data.

----------------------------------------------------------------------------
Radford M. Neal radford@xxxxxxxxxxxxxx
Dept. of Statistics and Dept. of Computer Science radford@xxxxxxxxxxxxxxxxxx
University of Toronto http://www.cs.utoronto.ca/~radford
----------------------------------------------------------------------------

.

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